{"id":"https://openalex.org/W2041025153","doi":"https://doi.org/10.1137/050637662","title":"Searching for Rare Growth Factors Using Multicanonical Monte Carlo Methods","display_name":"Searching for Rare Growth Factors Using Multicanonical Monte Carlo Methods","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2041025153","doi":"https://doi.org/10.1137/050637662","mag":"2041025153"},"language":"en","primary_location":{"id":"doi:10.1137/050637662","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050637662","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062904806","display_name":"Tobin A. Driscoll","orcid":"https://orcid.org/0000-0002-1490-2545"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tobin A. Driscoll","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054060676","display_name":"Kara L. Maki","orcid":"https://orcid.org/0000-0001-7364-1392"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kara L. Maki","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062904806"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4586,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.84018811,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"49","issue":"4","first_page":"673","last_page":"692"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.6731348037719727},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6057418584823608},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5950208306312561},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5109078288078308},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.50838702917099},{"id":"https://openalex.org/keywords/gaussian-elimination","display_name":"Gaussian elimination","score":0.46316397190093994},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.42737245559692383},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3870733976364136},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3605833649635315},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3520877957344055},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.29020625352859497},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2836889624595642},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17421427369117737},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1201925277709961},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.0944262444972992}],"concepts":[{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.6731348037719727},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6057418584823608},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5950208306312561},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5109078288078308},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.50838702917099},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.46316397190093994},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.42737245559692383},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3870733976364136},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3605833649635315},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3520877957344055},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.29020625352859497},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2836889624595642},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17421427369117737},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1201925277709961},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0944262444972992},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050637662","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050637662","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.158.4165","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.158.4165","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.udel.edu/~driscoll/pubs/growthfac2007.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1480928214","https://openalex.org/W1493921296","https://openalex.org/W1576347883","https://openalex.org/W1964136783","https://openalex.org/W1976662650","https://openalex.org/W1981745143","https://openalex.org/W1985093013","https://openalex.org/W1999202513","https://openalex.org/W2013737143","https://openalex.org/W2020804487","https://openalex.org/W2030911724","https://openalex.org/W2033900415","https://openalex.org/W2035811299","https://openalex.org/W2056760934","https://openalex.org/W2064071505","https://openalex.org/W2076092328","https://openalex.org/W2102862543","https://openalex.org/W2108207895","https://openalex.org/W2115780241","https://openalex.org/W2130416410","https://openalex.org/W2138309709","https://openalex.org/W2157959181","https://openalex.org/W2163924408","https://openalex.org/W2165917639","https://openalex.org/W2333159909","https://openalex.org/W2798909945","https://openalex.org/W3022136271","https://openalex.org/W4293282250"],"related_works":["https://openalex.org/W1969557273","https://openalex.org/W2023689870","https://openalex.org/W2913918688","https://openalex.org/W2170271555","https://openalex.org/W2952318043","https://openalex.org/W4281713237","https://openalex.org/W2078149201","https://openalex.org/W4381327231","https://openalex.org/W2102789413","https://openalex.org/W4210382808"],"abstract_inverted_index":{"The":[0],"growth":[1,12,57,118,145,164],"factor":[2,58,146,165],"of":[3,9,51,63,67,77,144,157,166,172],"a":[4,15,135,163,173],"matrix":[5,161],"quantifies":[6],"the":[7,61,65,142,155,170],"amount":[8],"potential":[10],"error":[11],"possible":[13],"when":[14],"linear":[16],"system":[17],"is":[18,28,168],"solved":[19],"using":[20,134],"Gaussian":[21],"elimination":[22],"with":[23,115,162],"row":[24],"pivoting.":[25],"While":[26],"it":[27],"an":[29,158],"easy":[30],"matter":[31],"[N.":[32,71],"J.":[33,37,40,72,91],"Higham":[34],"and":[35,69,75,86,102],"D.":[36,104],"Higham,":[38,73],"SIAM":[39,90],"Matrix":[41,92],"Anal.":[42,93],"Appl.,":[43,94],"10":[44],"(1989),":[45],"pp.":[46,97],"155\u2013164]":[47],"to":[48,60,127,140],"construct":[49],"examples":[50],"$n\\times":[52],"n$":[53],"matrices":[54,114,133],"having":[55],"any":[56],"up":[59],"maximum":[62],"$2^{n-1}$,":[64],"weight":[66],"experience":[68],"analysis":[70],"Accuracy":[74],"Stability":[76],"Numerical":[78,106],"Algorithms,":[79],"SIAM,":[80,109],"Philadelphia,":[81,110],"1996],":[82],"[L.":[83,99],"N.":[84,100],"Trefethen":[85,101],"R.":[87],"S.":[88],"Schreiber,":[89],"11":[95],"(1990),":[96],"335\u2013360],":[98],"I.":[103],"Bau,":[105],"Linear":[107],"Algebra,":[108],"1997]":[111],"suggest":[112],"that":[113,154],"exponentially":[116],"large":[117],"factors":[119],"are":[120],"exceedingly":[121],"rare.":[122],"Here":[123],"we":[124],"show":[125],"how":[126],"conduct":[128],"numerical":[129],"experiments":[130],"on":[131,169],"random":[132],"multicanonical":[136],"Monte":[137],"Carlo":[138],"method":[139],"explore":[141],"tails":[143],"probability":[147],"distributions.":[148],"Our":[149],"results":[150],"suggest,":[151],"for":[152],"example,":[153],"occurrence":[156],"$8\\times":[159],"8$":[160],"40":[167],"order":[171],"once-in-the-age-of-the-universe":[174],"event.":[175]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}